Jeremy has to cover 3 tanks completely with paint. Each tank is in the shape of a cylinder with a top and a bottom. The tank has a diameter of 1.6 m and a height of 1.8 m. Jeremy has 7 tins of paint. Each tin of paint covers 5 m². Has Jeremy got enough paint to cover completely the 3 tanks? You must show how you get your answer.

GCSE Edexcel Maths Powers, Roots & Standard Form: Jeremy has to cover 3 tanks comp

Jeremy has to cover 3 tanks completely with paint - Edexcel - GCSE Maths - Question 7 - 2019 - Paper 3

Question 7

Jeremy has to cover 3 tanks completely with paint. Each tank is in the shape of a cylinder with a top and a bottom. The tank has a diameter of 1.6 m and a height of... show full transcript

Worked Solution & Example Answer:Jeremy has to cover 3 tanks completely with paint - Edexcel - GCSE Maths - Question 7 - 2019 - Paper 3

Step 1

Calculate the Surface Area of One Tank

96%

114 rated

Answer

To find the surface area of a cylindrical tank, we use the formula:

$A = 2 \pi r(h + r)$

Where:

$r$ is the radius
$h$ is the height

The diameter of the tank is 1.6 m, so the radius $r$ is:

$r = \frac{1.6}{2} = 0.8 \text{ m}$

The height $h$ is given as 1.8 m. Plugging in these values:

$A = 2 \pi (0.8)(1.8 + 0.8) = 2 \pi (0.8)(2.6)$

Calculating the surface area: $A = 2 \pi (0.8)(2.6) = 2 \times 3.14 \times 0.8 \times 2.6 \approx 13.10 \text{ m}²$

Step 2

Calculate the Total Surface Area for Three Tanks

99%

104 rated

Answer

Since Jeremy has three tanks, the total surface area (TSA) is:

$TSA = 3 \times A$

Substituting in the previously calculated surface area:

$TSA = 3 \times 13.10 \approx 39.30 \text{ m}²$

Step 3

Calculate the Total Coverage Provided by Paint

96%

101 rated

Answer

Each tin of paint covers 5 m². Therefore, for 7 tins, the total coverage is:

$\text{Total Coverage} = 7 \times 5 = 35 \text{ m}²$

Step 4

Determine if There is Enough Paint

98%

120 rated

Answer

To see if Jeremy has enough paint, we compare the total coverage provided by the paint to the total surface area required:

Total surface area of tanks = 39.30 m²
Total coverage of paint = 35 m²

Since 35 m² < 39.30 m², Jeremy does not have enough paint to cover the three tanks completely.

Jeremy has to cover 3 tanks completely with paint - Edexcel - GCSE Maths - Question 7 - 2019 - Paper 3

Worked Solution & Example Answer:Jeremy has to cover 3 tanks completely with paint - Edexcel - GCSE Maths - Question 7 - 2019 - Paper 3

Calculate the Surface Area of One Tank

Calculate the Total Surface Area for Three Tanks

Calculate the Total Coverage Provided by Paint

Determine if There is Enough Paint

Join the GCSE students using SimpleStudy...